The author of the excerpt that you posted is quite correct that a person can "rotate between different places of residence", but they can't be a "Dual Resident" (except for the special case identified by the BATF). The author of the excerpt wrote correctly, even if misleadingly, by using a common legal tactic of first saying what you want the reader to believe (There can be a "Dual Resident"), then using the conjunctive "or", followed by what the law actually says (one can quickly change residency). You're led to believe that both are correct when technically, only one need be correct to make the whole statement correct. They actually teach law students how to do this (stuff) in their "Trial Advocacy" classes.
Let's look at the actual definition of "State of Residence" (Quoted from 27CFR478.11):
"State of Residence - The State in which an individual resides. An individual resides in a State if he or she is present in a State with the intention of making a home in that State. If an individual is on active duty as a member of the Armed Forces, the individual's State of residence is the State in which his or her permanent duty station is located, as stated in 18 U.S.C. 921(b). The following are examples that illustrate this definition:
Example 1.
A maintains a home in State X. A travels to State Y on a hunting, fishing, business, or other type of trip. A does not become a resident of State Y by reason of such trip.
Example 2.
A maintains a home in State X and a home in State Y. A resides in State X except for weekends or the summer months of the year and in State Y for the weekends or the summer months of the year. During the time that A actually resides in State X, A is a resident of State X, and during the time that A actually resides in State Y, A is a resident of State Y.
Example 3.
A, an alien, travels to the United States on a three-week vacation to State X. A does not have a state of residence in State X because A does not have the intention of making a home in State X while on vacation. This is true regardless of the length of the vacation.
Example 4.
A, an alien, travels to the United States to work for three years in State X. A rents a home in State X, moves his personal possessions into the home, and his family resides with him in the home. A intends to reside in State X during the 3-year period of his employment. A is a resident of State X."
First, note carefully the requirement that a person be "present in a state" in order to be a resident of that state. That condition alone makes "Dual Residency" quite impossible (unless one is standing on the stateline with a foot in each state). But then when you look at the examples, and particularly Example 2, it's pretty clear that a person who maintains homes in two states can change their residency as quickly as they can move between their two homes. A lot of folks liken this to being a "Dual Resident" of both states. But when you examine the wording, it's clear that they are not. They are only a singular resident of the state they're currently in.
Example 4 is highly relevant to the OP's situation. I would have to think that application of this example would hold him to be a resident of Kansas for the 18 months he plans to be there.